Childcare Cost Analysis

INFO 523 - Project 1

Author

Devendran Vemula

Abstract

The project investigates the intricate dynamics between childcare costs, unemployment rates, and poverty levels across various regions in the United States. Utilizing two primary datasets—the National Database of Childcare Prices (NDCP) and a comprehensive Counties Dataset—the analysis employs spatial mapping techniques to visualize mean unemployment rates and family poverty rates, as well as correlations between unemployment rates and poverty levels at the county and state levels. The findings reveal significant regional variations in unemployment rates, highlighting gender disparities, and underscore the correlation between unemployment rates and poverty levels. Furthermore, the project identifies regions with elevated family poverty rates and explores the relationship between family poverty rates and cumulative childcare costs. The results emphasize the economic challenges faced by families, especially in areas where childcare expenses intersect with high poverty rates. The project concludes with insights into future trends and the potential for integrating predictive modeling techniques and qualitative research methods to inform more effective policy interventions aimed at supporting families across the nation.

Introduction

The United States faces persistent challenges related to childcare affordability, unemployment rates, and poverty levels, which have profound implications for family well-being and economic stability. Understanding the complex interplay between these factors is crucial for policymakers, researchers, and practitioners seeking to develop effective interventions to support families and communities.

This project aims to investigate the multifaceted relationship between childcare costs, unemployment rates, and poverty levels across diverse regions in the United States. Two primary datasets are utilized: the National Database of Childcare Prices (NDCP), providing comprehensive childcare price data spanning from 2008 to 2018, and a Counties Dataset offering geographical and demographic insights.

The analysis approach involves utilizing spatial mapping techniques to visualize mean unemployment rates, family poverty rates, and correlations between unemployment rates and poverty levels at both the county and state levels. By leveraging these datasets and visualization methods, the project seeks to uncover regional disparities in unemployment rates, gender discrepancies, and the economic burden faced by families due to childcare expenses.

The insights generated from this investigation have the potential to inform policymakers, researchers, and stakeholders about the socio-economic challenges faced by families across different regions of the United States. By understanding these dynamics, policymakers can develop targeted interventions to alleviate economic hardships and promote greater equity and prosperity for families nationwide.

Dataset Information

1. Childcare Costs Dataset

  • Source: The National Database of Childcare Prices (NDCP)
  • Description: This dataset is the most comprehensive federal source of childcare prices at the county level. It provides childcare price data by childcare provider type, age of children, and county characteristics. The data spans from 2008 to 2018, offering estimates of childcare prices at the county level for different age groups and care settings, including home-based and center-based providers.

2. Counties Dataset

  • Description: This dataset contains geographical information for each county, and it will be used for spatial plotting.

Question

Analyze factors affecting childcare costs across counties and predict high-cost regions.

Number of ROWs and COLUMNs before cleaning data

Total Rows:  34567 
Total Columns:  61

Data Cleaning

Removed the unwanted rows by removing all NA and error data.

Data Exploration

Rows: 23,342
Columns: 61
$ county_fips_code          <int> 1001, 1001, 1001, 1001, 1001, 1001, 1001, 10…
$ study_year                <int> 2008, 2009, 2010, 2011, 2012, 2013, 2014, 20…
$ unr_16                    <dbl> 5.42, 5.93, 6.21, 7.55, 8.60, 9.39, 8.50, 7.…
$ funr_16                   <dbl> 4.41, 5.72, 5.57, 8.13, 8.88, 10.31, 9.18, 8…
$ munr_16                   <dbl> 6.32, 6.11, 6.78, 7.03, 8.29, 8.56, 7.95, 6.…
$ unr_20to64                <dbl> 4.6, 4.8, 5.1, 6.2, 6.7, 7.3, 6.8, 5.9, 4.4,…
$ funr_20to64               <dbl> 3.5, 4.6, 4.6, 6.3, 6.4, 7.6, 6.8, 6.1, 4.6,…
$ munr_20to64               <dbl> 5.6, 5.0, 5.6, 6.1, 7.0, 7.0, 6.8, 5.9, 4.3,…
$ flfpr_20to64              <dbl> 68.9, 70.8, 71.3, 70.2, 70.6, 70.7, 69.9, 68…
$ flfpr_20to64_under6       <dbl> 66.9, 63.7, 67.0, 66.5, 67.1, 67.5, 65.2, 66…
$ flfpr_20to64_6to17        <dbl> 79.59, 78.41, 78.15, 77.62, 76.31, 75.91, 75…
$ flfpr_20to64_under6_6to17 <dbl> 60.81, 59.91, 59.71, 59.31, 58.30, 58.00, 57…
$ mlfpr_20to64              <dbl> 84.0, 86.2, 85.8, 85.7, 85.7, 85.0, 84.2, 82…
$ pr_f                      <dbl> 8.5, 7.5, 7.5, 7.4, 7.4, 8.3, 9.1, 9.3, 9.4,…
$ pr_p                      <dbl> 11.5, 10.3, 10.6, 10.9, 11.6, 12.1, 12.8, 12…
$ mhi_2018                  <dbl> 58462.55, 60211.71, 61775.80, 60366.88, 5915…
$ me_2018                   <dbl> 32710.60, 34688.16, 34740.84, 34564.32, 3432…
$ fme_2018                  <dbl> 25156.25, 26852.67, 27391.08, 26727.68, 2796…
$ mme_2018                  <dbl> 41436.80, 43865.64, 46155.24, 45333.12, 4427…
$ total_pop                 <int> 49744, 49584, 53155, 53944, 54590, 54907, 55…
$ one_race                  <dbl> 98.1, 98.6, 98.5, 98.5, 98.5, 98.6, 98.7, 98…
$ one_race_w                <dbl> 78.9, 79.1, 79.1, 78.9, 78.9, 78.3, 78.0, 77…
$ one_race_b                <dbl> 17.7, 17.9, 17.9, 18.1, 18.1, 18.4, 18.6, 18…
$ one_race_i                <dbl> 0.4, 0.4, 0.3, 0.2, 0.3, 0.3, 0.4, 0.4, 0.4,…
$ one_race_a                <dbl> 0.4, 0.6, 0.7, 0.7, 0.8, 1.0, 0.9, 1.0, 0.8,…
$ one_race_h                <dbl> 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1,…
$ one_race_other            <dbl> 0.7, 0.7, 0.6, 0.5, 0.4, 0.7, 0.7, 0.9, 1.4,…
$ two_races                 <dbl> 1.9, 1.4, 1.5, 1.5, 1.5, 1.4, 1.3, 1.6, 2.0,…
$ hispanic                  <dbl> 1.8, 2.0, 2.3, 2.4, 2.4, 2.5, 2.5, 2.6, 2.6,…
$ households                <int> 18373, 18288, 19718, 19998, 19934, 20071, 20…
$ h_under6_both_work        <int> 1543, 1475, 1569, 1695, 1714, 1532, 1557, 13…
$ h_under6_f_work           <int> 970, 964, 1009, 1060, 938, 880, 1191, 1258, …
$ h_under6_m_work           <int> 22, 16, 16, 106, 120, 161, 159, 211, 109, 10…
$ h_under6_single_m         <int> 995, 1099, 1110, 1030, 1095, 1160, 954, 883,…
$ h_6to17_both_work         <int> 4900, 5028, 5472, 5065, 4608, 4238, 4056, 40…
$ h_6to17_fwork             <int> 1308, 1519, 1541, 1965, 1963, 1978, 2073, 20…
$ h_6to17_mwork             <int> 114, 92, 113, 246, 284, 354, 373, 551, 322, …
$ h_6to17_single_m          <int> 1966, 2305, 2377, 2299, 2644, 2522, 2269, 21…
$ emp_m                     <dbl> 27.40, 29.54, 29.33, 31.17, 32.13, 31.74, 32…
$ memp_m                    <dbl> 24.41, 26.07, 25.94, 26.97, 28.59, 27.44, 28…
$ femp_m                    <dbl> 30.68, 33.40, 33.06, 35.96, 36.09, 36.61, 37…
$ emp_service               <dbl> 17.06, 15.81, 16.92, 16.18, 16.09, 16.72, 16…
$ memp_service              <dbl> 15.53, 14.16, 15.09, 14.21, 14.71, 13.92, 13…
$ femp_service              <dbl> 18.75, 17.64, 18.93, 18.42, 17.63, 19.89, 20…
$ emp_sales                 <dbl> 29.11, 28.75, 29.07, 27.56, 28.39, 27.22, 25…
$ memp_sales                <dbl> 15.97, 17.51, 17.82, 17.74, 17.79, 17.38, 15…
$ femp_sales                <dbl> 43.52, 41.25, 41.43, 38.76, 40.26, 38.36, 36…
$ emp_n                     <dbl> 13.21, 11.89, 11.57, 10.72, 9.02, 9.27, 9.38…
$ memp_n                    <dbl> 22.54, 20.30, 19.86, 18.28, 16.03, 16.79, 17…
$ femp_n                    <dbl> 2.99, 2.52, 2.45, 2.09, 1.19, 0.77, 0.58, 0.…
$ emp_p                     <dbl> 13.22, 14.02, 13.11, 14.38, 14.37, 15.04, 16…
$ memp_p                    <dbl> 21.55, 21.96, 21.28, 22.80, 22.88, 24.48, 24…
$ femp_p                    <dbl> 4.07, 5.19, 4.13, 4.77, 4.84, 4.36, 6.07, 7.…
$ mcsa                      <dbl> 80.92, 83.42, 85.92, 88.43, 90.93, 93.43, 95…
$ mfccsa                    <dbl> 81.40, 85.68, 89.96, 94.25, 98.53, 102.82, 1…
$ mc_infant                 <dbl> 104.95, 105.11, 105.28, 105.45, 105.61, 105.…
$ mc_toddler                <dbl> 104.95, 105.11, 105.28, 105.45, 105.61, 105.…
$ mc_preschool              <dbl> 85.92, 87.59, 89.26, 90.93, 92.60, 94.27, 95…
$ mfcc_infant               <dbl> 83.45, 87.39, 91.33, 95.28, 99.22, 103.16, 1…
$ mfcc_toddler              <dbl> 83.45, 87.39, 91.33, 95.28, 99.22, 103.16, 1…
$ mfcc_preschool            <dbl> 81.40, 85.68, 89.96, 94.25, 98.53, 102.82, 1…

Number of ROWs and COLUMNs after cleaning data

Total Rows:  23342 
Total Columns:  61

Selecting only revelent column that need for project

We removed all rows where the study year is greater than 2015 due to the limited data available. This ensures more accurate analysis by focusing on years with sufficient data.

 county_fips_code   study_year       unr_16          funr_16      
 Min.   : 1001    Min.   :2016   Min.   : 0.000   Min.   : 0.000  
 1st Qu.:21015    1st Qu.:2016   1st Qu.: 4.370   1st Qu.: 4.010  
 Median :37029    Median :2017   Median : 6.100   Median : 5.730  
 Mean   :32996    Mean   :2017   Mean   : 6.436   Mean   : 6.119  
 3rd Qu.:48004    3rd Qu.:2018   3rd Qu.: 7.990   3rd Qu.: 7.730  
 Max.   :56045    Max.   :2018   Max.   :29.930   Max.   :31.440  
    munr_16          mhi_2018        total_pop          mc_infant     
 Min.   : 0.000   Min.   : 19842   Min.   :      74   Min.   : 53.58  
 1st Qu.: 4.420   1st Qu.: 42290   1st Qu.:   11205   1st Qu.:116.90  
 Median : 6.300   Median : 49351   Median :   27051   Median :144.96  
 Mean   : 6.722   Mean   : 51113   Mean   :  107294   Mean   :155.35  
 3rd Qu.: 8.390   3rd Qu.: 57094   3rd Qu.:   70291   3rd Qu.:175.00  
 Max.   :39.740   Max.   :136268   Max.   :10105722   Max.   :470.00  
   mc_toddler      mc_preschool     mfcc_infant      mfcc_toddler   
 Min.   : 49.39   Min.   : 49.39   Min.   : 47.56   Min.   : 46.97  
 1st Qu.:110.00   1st Qu.:102.50   1st Qu.: 97.05   1st Qu.: 91.10  
 Median :130.69   Median :121.91   Median :112.50   Median :110.00  
 Mean   :139.65   Mean   :130.15   Mean   :120.55   Mean   :114.05  
 3rd Qu.:157.00   3rd Qu.:146.54   3rd Qu.:135.54   3rd Qu.:127.50  
 Max.   :419.00   Max.   :385.00   Max.   :430.94   Max.   :376.32  
 mfcc_preschool        pr_f      
 Min.   : 40.03   Min.   : 0.00  
 1st Qu.: 90.00   1st Qu.: 7.60  
 Median :106.68   Median :10.60  
 Mean   :111.19   Mean   :11.57  
 3rd Qu.:125.00   3rd Qu.:14.30  
 Max.   :331.34   Max.   :52.10

Number of ROWs and COLUMNs after selecting only relevent data.

Total Rows:  7384 
Total Columns:  14 
county_fips_code       study_year           unr_16          funr_16 
               0                0                0                0 
         munr_16         mhi_2018        total_pop        mc_infant 
               0                0                0                0 
      mc_toddler     mc_preschool      mfcc_infant     mfcc_toddler 
               0                0                0                0 
  mfcc_preschool             pr_f 
               0                0

Univariate Analysis (Histograms & Boxplots)

- Distribution of Childcare Costs (Infant, Toddler, Preschool):
- Boxplot of Unemployment Rates (unr_16, funr_16, munr_16):
  1. Spatial Analysis: Interactive Map for Childcare Costs by County
'data.frame':   7384 obs. of  14 variables:
 $ county_fips_code: int  1001 1001 1001 1003 1003 1003 1005 1005 1005 1007 ...
 $ study_year      : int  2016 2017 2018 2016 2017 2018 2016 2017 2018 2016 ...
 $ unr_16          : num  5.59 5.21 4.23 6.29 5.5 ...
 $ funr_16         : num  6.27 5.84 3.41 6.48 5.49 ...
 $ munr_16         : num  4.99 4.64 4.93 6.12 5.52 ...
 $ mhi_2018        : num  55754 56977 58786 53933 54139 ...
 $ total_pop       : int  55049 55036 55200 199510 203360 208107 26614 26201 25782 22572 ...
 $ mc_infant       : num  113 117 120 113 117 ...
 $ mc_toddler      : num  113 117 120 113 117 ...
 $ mc_preschool    : num  98.7 100.1 101.5 105.7 108.5 ...
 $ mfcc_infant     : num  107 107 107 106 107 ...
 $ mfcc_toddler    : num  107 107 107 106 107 ...
 $ mfcc_preschool  : num  107 106 106 106 107 ...
 $ pr_f            : num  9.4 10.9 12 9.3 8.2 7.3 20 20.5 21.5 11.7 ...
  1. Association Analysis

  • Purpose:

    The numeric columns (unr_16, funr_16, etc.) are discretized into categorical bins using the cut() function. For example: Low: Bottom third of values. Medium: Middle third of values. High: Top third of values. The result is a dataset of categorical variables suitable for association rule mining.

  • Columns selected:

    Unemployment rates (unr_16, funr_16, munr_16), median household income (mhi_2018), and total population (total_pop).

transactions as itemMatrix in sparse format with
 7384 rows (elements/itemsets/transactions) and
 15 columns (items) and a density of 0.3333333 

most frequent items:
total_pop=Low   munr_16=Low   funr_16=Low    unr_16=Low  mhi_2018=Low 
         7372          7062          6769          6588          5796 
      (Other) 
         3333 

element (itemset/transaction) length distribution:
sizes
   5 
7384 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      5       5       5       5       5       5 

includes extended item information - examples:
         labels variables levels
1    unr_16=Low    unr_16    Low
2 unr_16=Medium    unr_16 Medium
3   unr_16=High    unr_16   High

includes extended transaction information - examples:
  transactionID
1             1
2             2
3             3
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
        0.5    0.1    1 none FALSE            TRUE       5    0.01      1
 maxlen target  ext
     10  rules TRUE

Algorithmic control:
 filter tree heap memopt load sort verbose
    0.1 TRUE TRUE  FALSE TRUE    2    TRUE

Absolute minimum support count: 73 

set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[15 item(s), 7384 transaction(s)] done [0.00s].
sorting and recoding items ... [9 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 5 done [0.00s].
writing ... [232 rule(s)] done [0.00s].
creating S4 object  ... done [0.00s].
     lhs                  rhs                support confidence   coverage     lift count
[1]  {funr_16=Medium,                                                                    
      munr_16=Medium}  => {unr_16=Medium} 0.02153304  0.9695122 0.02221018 9.321456   159
[2]  {funr_16=Medium,                                                                    
      munr_16=Medium,                                                                    
      total_pop=Low}   => {unr_16=Medium} 0.02153304  0.9695122 0.02221018 9.321456   159
[3]  {funr_16=Medium,                                                                    
      munr_16=Medium,                                                                    
      mhi_2018=Low}    => {unr_16=Medium} 0.02126219  0.9691358 0.02193933 9.317837   157
[4]  {funr_16=Medium,                                                                    
      munr_16=Medium,                                                                    
      mhi_2018=Low,                                                                      
      total_pop=Low}   => {unr_16=Medium} 0.02126219  0.9691358 0.02193933 9.317837   157
[5]  {munr_16=Medium}  => {unr_16=Medium} 0.03819068  0.9126214 0.04184724 8.774474   282
[6]  {munr_16=Medium,                                                                    
      total_pop=Low}   => {unr_16=Medium} 0.03819068  0.9126214 0.04184724 8.774474   282
[7]  {funr_16=Low,                                                                       
      munr_16=Medium}  => {unr_16=Medium} 0.01665764  0.9111111 0.01828277 8.759954   123
[8]  {funr_16=Low,                                                                       
      munr_16=Medium,                                                                    
      total_pop=Low}   => {unr_16=Medium} 0.01665764  0.9111111 0.01828277 8.759954   123
[9]  {munr_16=Medium,                                                                    
      mhi_2018=Low}    => {unr_16=Medium} 0.03737811  0.9108911 0.04103467 8.757838   276
[10] {munr_16=Medium,                                                                    
      mhi_2018=Low,                                                                      
      total_pop=Low}   => {unr_16=Medium} 0.03737811  0.9108911 0.04103467 8.757838   276
Available control parameters (with default values):
layout   =  stress
circular     =  FALSE
ggraphdots   =  NULL
edges    =  <environment>
nodes    =  <environment>
nodetext     =  <environment>
colors   =  c("#EE0000FF", "#EEEEEEFF")
engine   =  ggplot2
max  =  100
verbose  =  FALSE

Eclat Algorithm

transactions as itemMatrix in sparse format with
 7384 rows (elements/itemsets/transactions) and
 15 columns (items) and a density of 0.3333333 

most frequent items:
total_pop=Low   munr_16=Low   funr_16=Low    unr_16=Low  mhi_2018=Low 
         7372          7062          6769          6588          5796 
      (Other) 
         3333 

element (itemset/transaction) length distribution:
sizes
   5 
7384 

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      5       5       5       5       5       5 

includes extended item information - examples:
         labels variables levels
1    unr_16=Low    unr_16    Low
2 unr_16=Medium    unr_16 Medium
3   unr_16=High    unr_16   High

includes extended transaction information - examples:
  transactionID
1             1
2             2
3             3
Eclat

parameter specification:
 tidLists support minlen maxlen            target  ext
    FALSE    0.01      1      5 frequent itemsets TRUE

algorithmic control:
 sparse sort verbose
      7   -2    TRUE

Absolute minimum support count: 73 

create itemset ... 
set transactions ...[15 item(s), 7384 transaction(s)] done [0.00s].
sorting and recoding items ... [9 item(s)] done [0.00s].
creating bit matrix ... [9 row(s), 7384 column(s)] done [0.00s].
writing  ... [111 set(s)] done [0.00s].
Creating S4 object  ... done [0.00s].
     items                                     support   count
[1]  {total_pop=Low}                           0.9983749 7372 
[2]  {munr_16=Low}                             0.9563922 7062 
[3]  {munr_16=Low, total_pop=Low}              0.9547671 7050 
[4]  {funr_16=Low}                             0.9167118 6769 
[5]  {funr_16=Low, total_pop=Low}              0.9150867 6757 
[6]  {funr_16=Low, munr_16=Low}                0.8982936 6633 
[7]  {funr_16=Low, munr_16=Low, total_pop=Low} 0.8966685 6621 
[8]  {unr_16=Low}                              0.8921993 6588 
[9]  {unr_16=Low, total_pop=Low}               0.8905742 6576 
[10] {unr_16=Low, munr_16=Low}                 0.8905742 6576 

Available control parameters (with default values):
layout   =  stress
circular     =  FALSE
ggraphdots   =  NULL
edges    =  <environment>
nodes    =  <environment>
nodetext     =  <environment>
colors   =  c("#EE0000FF", "#EEEEEEFF")
engine   =  ggplot2
max  =  100
verbose  =  FALSE

Explanation of Code

- Discretization:
    The numeric columns are divided into "Low," "Medium," and "High" categories using cut().

- Transactions Conversion:
    Convert the preprocessed data into a transaction format, required by arules.

- Eclat Algorithm:
    eclat() generates frequent itemsets based on support.
    Parameters:
        supp = 0.01: Minimum support threshold (at least 1% of transactions must contain the itemset).
        maxlen = 5: Maximum length of itemsets.

- Frequent Itemsets:
    The output includes the most frequently occurring combinations of items.

- Visualization:
    Item Frequency Plot: Displays the most frequent single items.
    Graph-Based Visualization: Shows relationships among items within frequent itemsets.
    Scatterplot: Highlights the support of frequent itemsets.

Visualizations

Top 10 Frequent Items:
    Bar plot showing the frequency of the most common items.

Graph Plot:
    A network plot where nodes represent items, and edges indicate their co-occurrence in frequent itemsets.

Scatterplot:
    Displays itemsets by their support.

K-medoids clustering

Medoids:
       ID unr_16 funr_16 munr_16 mhi_2018 total_pop
[1,] 7384      1       1       1        1         1
[2,] 7383      1       1       1        2         1
[3,] 7092      2       2       1        1         1
Clustering vector:
   [1] 1 1 2 1 1 1 3 3 1 1 1 1 1 1 1 3 3 3 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 3 3
  [38] 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 1 3 3 1 1 1 1 1 1 1 3 3 1 3 3 3 1 1
  [75] 1 1 1 2 3 3 3 1 1 1 1 1 1 3 1 1 3 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1
 [112] 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 2 2 2 3 3 3 1 1 1 1 1 1 1 1 1 3
 [149] 3 3 1 1 1 1 1 1 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 3 1 1 1
 [186] 3 1 1 1 3 3 1 3 3 1 3 3 3 1 3 1 2 2 2 3 3 3 1 1 1 1 1 1 3 3 3 3 3 1 3 3 2
 [223] 3 3 1 1 2 2 3 3 1 3 3 3 1 1 1 1 1 1 3 3 3 1 1 1 3 3 3 1 1 1 3 3 1 1 1 1 2
 [260] 2 2 1 1 1 3 3 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
 [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 3 1 1 1 1 1 3 3 3 3 1 1 1
 [371] 3 3 1 1 1 2 2 1 1 1 1 3 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [408] 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 3 3 3 1 1 1
 [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 3 1 1 1 2 2 2 2 3 3 2
 [482] 2 2 3 1 1 1 1 1 3 1 1 2 2 2 3 1 1 2 2 2 3 3 1 3 1 1 1 1 1 3 3 3 1 1 1 3 3
 [519] 3 3 1 1 3 3 1 1 1 1 2 2 2 1 1 1 2 2 2 1 3 1 3 3 1 3 3 3 1 1 1 2 2 2 2 2 2
 [556] 2 2 2 2 2 2 2 2 2 2 2 2 3 1 1 3 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2
 [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 3 1 1 2 2 2 2 2 2 3 3 3 3 3 1 3 3
 [630] 1 1 1 1 3 3 1 3 1 1 2 2 2 2 2 2 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
 [667] 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1 1 1 2 1 1 3 1 1 1 1 1 3 1 3 1 3 1 2 2 2 2
 [704] 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 3 1 3 3 3 1 3 3 1 1 3 3 3 1 3 3 1
 [741] 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1 1 2 2 2 2 2 2 3 1 1 1 1 1 1 2
 [778] 1 1 1 1 1 1 3 3 2 2 1 1 2 2 1 1 2 2 1 1 3 1 1 1 1 1 1 2 1 1 1 3 1 1 1 1 1
 [815] 1 1 1 1 3 3 1 1 3 2 1 1 1 3 3 1 3 1 3 1 3 3 2 1 3 3 3 2 1 1 2 1 2 1 3 1 2
 [852] 1 1 3 3 3 2 1 1 2 1 3 1 1 2 1 2 1 2 1 1 1 1 3 1 2 1 1 3 3 2 1 3 2 1 1 1 1
 [889] 1 3 1 3 1 3 3 1 2 3 1 3 3 1 3 1 3 1 3 3 1 3 1 1 1 1 3 3 2 1 2 3 2 1 3 3 1
 [926] 3 3 1 1 3 3 3 1 3 3 3 3 3 1 3 1 3 1 3 3 1 3 1 1 3 1 1 1 3 1 1 1 3 3 3 1 3
 [963] 1 1 1 1 1 1 2 2 2 2 2 2 3 1 3 1 1 1 1 1 1 3 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1
[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1037] 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1
[1074] 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 2 1 2 1 1 1 1 1 1 3 3 1 1 1 1 3 1 1 1
[1111] 1 1 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1
[1148] 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1185] 3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2
[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 2
[1259] 1 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
[1296] 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 3 3 3
[1333] 3 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1370] 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 1
[1407] 2 2 2 1 1 1 1 1 2 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 2 2 1 1 1
[1444] 1 1 1 2 1 1 2 1 2 1 1 1 1 2 1 1 1 2 2 1 1 1 2 1 1 2 2 1 2 1 2 1 1 1 1 1 1
[1481] 1 1 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
[1518] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
[1555] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1592] 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1629] 1 1 1 2 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 2 2 2 1
[1666] 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1
[1703] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1
[1740] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 1 1 1 1 1 1
[1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 2 1
[1814] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2 2 2 1 1 1
[1851] 1 1 1 1 1 1 1 1 1 3 3 3 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 1 3
[1888] 3 1 1 1 1 3 1 1 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3 3 1 1
[1925] 1 1 1 1 3 3 3 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1962] 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 1 3 1 3 2
[1999] 2 2 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3 3 3 3 3 1 1 1 3 1 1 1 1 1 1 1
[2036] 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 1 1
[2073] 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 1 3 3 1
[2110] 1 1 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 1 1 2 2 2 2 2 2 1 1 1 2 2
[2147] 2 3 3 1 1 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 3 2 2 2
[2184] 1 1 2 1 3 1 3 1 1 1 3 2 1 3 3 3 1 3 1 3 3 1 3 1 1 1 1 1 1 1 3 2 3 1 3 1 1
[2221] 1 1 1 3 3 1 3 2 3 1 1 1 1 3 2 1 3 1 1 1 1 3 1 1 3 3 1 1 1 1 1 1 1 2 2 2 1
[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2
[2295] 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 3 1 1 2 2 2 1 1 1 2 2 2
[2332] 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 3 1 2 2 2 2 2 2 1 1 1 2 2 2 3 1 1 2
[2369] 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[2406] 2 2 2 2 3 1 1 1 1 1 1 2 2 1 1 1 1 1 1 3 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1
[2443] 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 3 3 3 2 2 2 3 3 1 1 1 1 1 1 1 2 2 2 1
[2480] 1 1 3 3 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 3 3 3 1 1 2 2 2 2 1 1 1 2 2 2 3 3 1
[2554] 3 3 1 2 2 2 3 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 3 3 3 3
[2591] 1 1 1 1 1 2 2 2 1 1 1 3 3 1 3 3 1 1 1 1 3 3 3 1 1 1 2 2 2 3 3 1 3 3 3 1 1
[2628] 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 1 1 1 1 1 1 2 2 2
[2665] 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 2 1 2 2 2 2 2 2 1
[2702] 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 2 2
[2739] 2 1 1 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
[2776] 2 2 2 1 1 1 1 1 1 2 2 2 3 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2
[2813] 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1 1 1 1
[2850] 1 1 1 1 2 2 2 1 1 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1
[2887] 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 3 1 1 1
[2924] 3 3 1 3 3 3 3 3 1 3 3 3 3 3 1 1 1 1 3 1 1 3 3 1 3 3 3 3 1 1 3 3 3 3 3 3 3
[2961] 3 3 3 3 3 2 2 2 3 3 3 3 3 1 1 1 1 3 3 3 1 3 1 1 1 1 1 1 1 3 1 1 3 3 3 3 3
[2998] 3 3 3 3 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1 1 1 1 3 1 1 1 1 1 1 3 3 1 1 1 3 1 1
[3035] 1 1 3 1 1 1 3 3 3 1 1 1 3 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3
[3072] 3 3 3 1 1 1 1 1 3 3 1 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 3 3 1 3 3 3 3 3
[3109] 3 1 1 1 1 1 1 3 3 3 3 3 3 1 1 1 3 1 1 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 3 3 3
[3146] 3 3 3 3 1 1 1 3 3 3 3 1 1 1 1 3 3 3 1 1 1 1 2 3 1 1 1 3 3 1 1 1 1 1 1 1 2
[3183] 1 1 1 1 2 1 3 1 1 1 2 1 1 2 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1 2
[3220] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3257] 1 1 1 1 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3294] 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3331] 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[3368] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1
[3405] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2
[3442] 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2
[3479] 2 1 1 1 1 1 1 3 3 3 1 1 1 2 2 2 1 2 2 1 1 1 1 1 1 1 2 2 3 1 2 2 3 3 1 1 2
[3516] 2 2 1 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 3 3 2 2 2 2 2 2 2 2
[3553] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
[3590] 3 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 2 1 3 1 1 1 1 1 2 1 1 2 2 1 1 2 2 2 1 1 1
[3627] 2 2 2 2 2 1 2 2 1 1 1 1 2 1 2 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1
[3664] 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 1 1 1 3 1 1 2 2 2 3 1 1 2 2 2 1 1 1 1 1 1
[3701] 2 2 2 1 1 1 3 3 3 3 1 1 3 3 1 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 3
[3738] 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1
[3775] 1 1 1 1 3 3 3 3 3 1 3 3 3 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 3 3 3 1 1 1 1 1 1
[3812] 1 1 1 1 1 1 3 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 3 1 2 2 2 1
[3849] 1 1 1 1 1 1 1 1 3 1 1 3 3 1 3 3 1 1 1 1 1 1 1 3 3 3 3 1 1 3 1 1 3 1 1 3 1
[3886] 1 1 3 1 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 2 2 2 3 3 1 2 2 2 1 1 1
[3923] 3 3 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
[3960] 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1
[3997] 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 2 1 2 1 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
[4034] 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 3
[4071] 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1
[4108] 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
[4145] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 2 2 2 2 1
[4182] 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1
[4219] 1 3 3 3 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1
[4256] 2 2 2 3 3 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4293] 1 1 2 2 2 3 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1
[4330] 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
[4367] 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1
[4404] 1 1 2 2 2 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4441] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
[4478] 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
[4515] 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4552] 1 1 1 1 3 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
[4589] 1 1 1 2 2 1 2 2 2 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 3 1 1 3 1 1 3 1 1 1 2 2 3
[4626] 1 1 3 1 1 1 1 1 3 3 3 2 2 2 1 1 1 3 3 3 3 1 1 3 1 1 3 3 1 1 1 1 1 1 1 1 1
[4663] 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
[4700] 3 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1
[4737] 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 2 2 2 2
[4774] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4811] 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2
[4848] 2 2 1 1 1 2 2 2 3 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[4885] 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 2 1 1 2 2 2 2 2 2 2 1 2 1 1 1 3 1 1 3 3 3 1
[4922] 1 1 1 1 1 3 3 1 2 2 2 1 1 2 1 1 1 1 2 2 1 1 1 3 1 1 3 1 3 3 3 3 3 1 1 3 3
[4959] 3 1 1 1 2 2 2 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 3 1 1 1 1 3 1 1 1 3 3 1 1 1 1
[4996] 1 1 1 1 1 1 3 1 1 1 2 2 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
[5033] 1 1 1 1 1 3 3 3 3 1 1 3 1 1 2 2 2 1 2 2 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1
[5070] 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 2 1
[5107] 3 3 3 1 1 1 2 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2
[5144] 2 2 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1
[5181] 1 1 2 2 1 1 2 3 1 1 1 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[5218] 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3
[5255] 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 1
[5292] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1
[5329] 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 3 1 3 3 3 3 3 1 1 1 1 1 1 1 3 3 1 1
[5366] 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 3 3 1 3 1 1 1 1 1 1 1 1 1 1
[5403] 1 1 1 1 3 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1
[5440] 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 1 1 3
[5477] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 2 2 1 1 1 3 3 1 1 1 1 3 3 3 1 1
[5514] 1 1 1 1 1 1 1 1 1 1 3 3 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2
[5551] 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1
[5588] 1 1 2 2 2 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1
[5625] 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
[5662] 3 3 3 1 1 1 2 2 2 1 1 1 1 1 1 2 2 1 1 3 3 3 3 3 2 2 2 1 1 1 3 3 1 1 1 1 1
[5699] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 3 3 3 3 3 1 1 1 3 3 3 1 1 1 2 2
[5736] 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 2 2 2 1 3 1
[5773] 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
[5810] 1 1 2 2 2 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 2 2 2 3 1 3 2 2
[5847] 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
[5884] 2 2 1 1 1 1 2 2 2 3 3 1 1 1 1 1 1 1 3 3 3 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2
[5921] 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[5958] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 2 2 1 1 1 1 1 1 1 2 2 2 1 1 1 3 1 1 1 1 1
[5995] 1 1 1 2 3 2 1 1 1 1 3 3 2 2 2 1 1 1 1 1 1 3 3 3 2 2 2 1 1 1 2 2 2 3 1 1 1
[6032] 1 1 1 1 1 1 1 1 2 2 2 1 1 1 3 1 1 3 3 3 1 1 1 3 3 1 3 3 1 1 1 1 1 1 1 1 3
[6069] 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 2 2
[6106] 2 2 2 1 1 1 1 1 1 1 1 1 1 1 3 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 3 3 1 1
[6143] 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 3 1 3 3 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1
[6180] 2 1 1 1 1 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 2 2 3 3 1
[6217] 3 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1
[6254] 1 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 2 2 2 1 1 2 2 2 2 1 1 1 2 2 2 1 1 1 3 3
[6291] 3 3 3 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
[6328] 1 2 2 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
[6365] 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2
[6402] 2 1 1 2 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 1 1 1 1
[6439] 1 1 1 2 2 2 2 2 2 1 1 3 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1
[6476] 1 1 1 1 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
[6513] 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2
[6550] 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 3 2 2 2 2 2 2 1 1 1 3 3 3 2 2 2 1 2 2 1
[6587] 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 2 1 1 1 2 2 2 1 1
[6624] 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2
[6661] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1
[6698] 1 1 3 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2 1 3 1 1 1 1 3 3 1 3 3
[6735] 3 2 2 2 2 2 2 3 3 3 1 2 2 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 2 2 2 2 2 2
[6772] 3 1 1 1 1 1 1 1 1 3 3 3 3 3 3 2 2 2 3 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
[6809] 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1
[6846] 1 1 1 2 1 1 1 2 2 2 1 1 1 1 1 1 3 3 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1
[6883] 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1
[6920] 1 1 2 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 3 1 3 3 3 1 1 1 1 1
[6957] 1 3 3 3 3 3 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[6994] 2 2 2 1 1 1 1 1 1 1 1 1 3 3 3 3 3 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3 3 3 1
[7031] 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1
[7068] 1 3 1 1 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1 1 3 3 3
[7105] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 1 1 1 2
[7142] 2 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1
[7179] 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
[7216] 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1
[7253] 2 2 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
[7290] 1 1 1 2 2 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
[7327] 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1
[7364] 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 1
Objective function:
    build      swap 
0.1099288 0.1099288 

Available components:
 [1] "medoids"    "id.med"     "clustering" "objective"  "isolation" 
 [6] "clusinfo"   "silinfo"    "diss"       "call"       "data"      

   1    2    3 
4887 1582  915

Explanation of Code: K-medoids Clustering:

Step 1: Discretize the numeric variables into categorical values.
Step 2: Convert the categorical columns to numeric values, which is required for clustering.
Step 3: Apply the pam() function, which performs K-medoids clustering, where k = 3 specifies the number of clusters.
Step 4: The result is visualized, and the clusters are added back to the original data for further inspection.

Plot Explanation:

Axes (Component 1 and Component 2):
    These are the principal components resulting from a dimensionality reduction process like PCA (Principal Component Analysis) applied to your dataset.
    Since your data likely has many variables, PCA simplifies the data into two components to visualize in a 2D space.

Clusters:
    The different shapes (e.g., triangle, circle, cross) represent different clusters identified by the K-medoids algorithm.
    Each shape corresponds to one of the three clusters (k = 3 in your case).

Ellipses:
    The ellipses around the clusters show the spread or variability of data points within each cluster.
    Tighter ellipses indicate that the points in the cluster are more compact and closely related.

Medoids (Cluster Centers):
    The cluster centers (medoids) are the most representative data points within each cluster. They are marked by the shapes at the center of each cluster.

Pink Lines:
    These lines connect data points to their respective medoids (cluster centers).
    They indicate the assignment of each data point to its cluster.

Explained Variability:
    The note at the bottom indicates that 64.61% of the variability in the dataset is explained by the two components plotted.
    While this is a decent percentage, it suggests that there might be additional variability captured in higher dimensions not represented here.

Hierarchical clustering


   1    2    3 
4873 1590  921

Hierarchical Clustering:

Step 1: Discretize the numeric variables into categorical values.
Step 2: Convert the categorical columns to numeric values, which is required for clustering.
Step 3: Compute the distance matrix using dist() with Euclidean distance. This matrix is then used to perform hierarchical clustering using hclust().
Step 4: The dendrogram is plotted to visualize the hierarchical clustering. You can specify the number of clusters using cutree().
Step 5: Cluster labels are added to the dataset, and the clusters can be inspected